The efficiency of thermodynamic systems used for converting thermal energy into work or other useful energy forms is most commonly limited by the theoretical Carnot cycle efficiency for cases of a constant working fluid operating in a thermal engine. However, more complex thermodynamic systems, such as fuel cells, can violate maximum Carnot cycle efficiencies for thermal engines by passing energy through a system where the working fluid chemically changes over time. Nevertheless, these systems are still limited in the most general sense to the assumption of operating near local thermodynamic equilibrium (quasi-equilibrium) at every point in the thermodynamic cycle.
Achieving thermodynamic equilibrium at a point in a thermodynamic cycle requires the rates of heat and mass transport (and chemical reaction for the cases of chemically reacting fluids) for equilibrating a system to be much faster than the rates of change that occur in the system. For example, in a gas piston, the molecular collision rates inside the gas for equilibrating the gas are typically very high relative to piston velocities. As a result, the bulk gas density, pressure and temperature effectively equilibrate almost instantaneously relative to the rate of piston motion, and therefore, the gas tends to remain in thermodynamic quasi-equilibrium (near equilibrium) at every spatial location occupied by the gas. Accordingly, the thermodynamic equilibrium assumption remains valid, and the efficiency of the thermodynamic system remains constrained within the traditional limit.